Exact controllability for the semilinear string equation in non cylindrical domains

• Autorzy: Araruna F. D. , Antunes G. O. , Medeiros L. A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).

Słowa kluczowe

EN

exact controllability; string equation; semilinear; non cylindrical

PL

sterowność; półliniowość

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2004
• Tom: Vol. 33, no 2
• Strony: 237--257
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Araruna F. D.

• Instituto de Matematica Universidade Federal do Rio de Janeiro Caixa Postal 68530 21945-970, Rio de Janeiro-RJ, Brasil

autor

Antunes G. O.

• Instituto de Matematica Universidade Federal do Rio de Janeiro Caixa Postal 68530 21945-970, Rio de Janeiro-RJ, Brasil

autor

Medeiros L. A.

• Instituto de Matematica Universidade Federal do Rio de Janeiro Caixa Postal 68530 21945-970, Rio de Janeiro-RJ, Brasil

Bibliografia

• Kangsheng, L. and Yong, J. (1999) Rapid Exact Controllability of the Wave Equation by Controls Distributed on a Time-Variant Subdomain. Chinese Ann. of Math. 20B(1), 65–76.
• Kapitonov, B.V. (1994) Uniform Stabilization and Simultaneous Exac tBoundary Controllability for a Par of Hyperbolic Systems. Siberian Mathematical Journal 35(4), 722–734.
• Komornik, V. (1994) Exact Controllability and Stabilization (The Multiplier Method). Masson, Paris.
• Lions, J.L. (1988) Controlabilit́e Exacte, Perturbation et Stabilisation de Systemes Distribúees. Tome I, Controlabilit́e Exacte, Masson, RMAB, Paris.
• Lions, J.L. (1988) Exact Controllability, Stabilization and Pertubation for Distributed Systems. SIAM Rev. 30, 1–68.
• Medeiros, L.A. (1993) Exact Controllability for a Timoshenko Model of Vibrations of Beams. Advances in Mathematical Sciences and Applications 2(1), 47–61.
• Medeiros, L.A., Limaco, J. and Menezes, S.B. (2002) Vibrations of Elastic Strings (Mathematical Aspects). Journal of Computational Analysisand Applications, Part 1,4(2), 91–127; Part 2,4(3), 212–263.
• Milla Miranda, M. (1995) HUM and Wave Equation with Variable Coefficients.Asymptotic Analysis 11, 317–341.
• Zuazua, E. (1990) An a Introduction to the Exact Controllability for Distributed Systems. CMFA, Universidade de Lisboa, Portugal.
• Zuazua, E. (1990) Exact Controllability for the Semilinear Wave Equation. J. Math. Pures et Appl.69, 1-31.